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Spring question

  1. Dec 16, 2004 #1
    there's a 3kg mass on a 30 degree frictionless incline. The mass travels d distance and hits a spring with k=400N/m. The spring contracts 0.2 m and brings the block to a stop.

    I need to find the distance the block traveled.

    F=kx
    F=400*.2
    F=80N

    so the block has to hit with 80N.
    what formula would I use to get distance? I am confused because if I used any energy formula (which I know I will have to) the question is in Joules instead of Newtons. What should I do?
     
  2. jcsd
  3. Dec 16, 2004 #2
    You can solve this with energy.
    At any point on the block's path you can find its energy with the equation
    [tex] E = .5kx^2 + .5mv^2 + mgy [/tex]

    Consider when the spring has been fully compressed to be y=0. Can you do it from there? Note: y does not equal d.
     
  4. Dec 16, 2004 #3
    are you saying that:
    E=80N+.5mv^2 ?
     
  5. Dec 16, 2004 #4
    Heres the easiest way to solve the problem:
    We know the spring compressed .2 meters. How much energy did the block impart to the spring to do this? We can find out using the potential energy of a spring formula [tex] E = .5kx^2 [/tex] Under the conservation of energy, the potential energy of the block at the top of the ramp must be equal to the PE of the spring. Use [tex] E = mgy [/tex] to find y and then use trigonometry to find the hypotonuese of the triangle.
    Remember : the key to sucsess in physics is thinking; not memorizing how to do every possible problem.
     
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